What is the derivative of sin^{ln(x}(x)) ?

The derivative of sin^{ln(x}(x)) is x^{ln(sin(x))}((ln(sin(x)))/x+cot(x)ln(x))

What is the first derivative of sin^{ln(x}(x)) ?

The first derivative of sin^{ln(x}(x)) is x^{ln(sin(x))}((ln(sin(x)))/x+cot(x)ln(x))

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\frac{d}{d x} (sin^{l n (x)} (x))

x^{l n (s i n (x))} (\frac{ln ( sin ( x ) )}{x} + cot (x) ln (x))

Solution steps

\frac{d}{d x} (sin^{l n (x)} (x))

Apply exponent rule:

a^{b} = e^{b l n (a)}

sin^{l n (x)} (x) = e^{l n (x) l n (s i n (x))}

= \frac{d}{d x} (e^{l n (x) l n (s i n (x))})

Apply the chain rule:

e^{l n (x) l n (s i n (x))} \frac{d}{d x} (ln (x) ln (sin (x)))

= e^{l n (x) l n (s i n (x))} \frac{d}{d x} (ln (x) ln (sin (x)))

\frac{d}{d x} (ln (x) ln (sin (x))) = \frac{ln ( sin ( x ) )}{x} + cot (x) ln (x)

= e^{l n (x) l n (s i n (x))} (\frac{ln ( sin ( x ) )}{x} + cot (x) ln (x))

e^{l n (x) l n (s i n (x))} = x^{l n (s i n (x))}

= x^{l n (s i n (x))} (\frac{ln ( sin ( x ) )}{x} + cot (x) ln (x))

x \to 2 lim (5 x + 1)

\frac{\partial}{\partial y} ((x^{2} + y^{2})^{\frac{4}{5}})

f (x) = x^{2} - x + 13, at x = 4

f (x) = - \frac{4}{3} x^{\frac{2}{3}}

(y^{2} + 1) d x = y \cdot sec^{2} (x) d y

What is the derivative of sin^{ln(x}(x)) ?
The derivative of sin^{ln(x}(x)) is x^{ln(sin(x))}((ln(sin(x)))/x+cot(x)ln(x))
What is the first derivative of sin^{ln(x}(x)) ?
The first derivative of sin^{ln(x}(x)) is x^{ln(sin(x))}((ln(sin(x)))/x+cot(x)ln(x))